I thought the concept of a price weighted index was pretty simple until I read this sentence in the CFAI books:
“A price-weighted index can be interpreted as a portfolio composed of one share of each constituent security”
How someone please help me understand what this means? Specifically, how is this different from an equally weighted index?
If an index has only two constituent securities (A and B), and the prices are
Price of A = $20
Price of B = $30
The price-weighted index = ($20 + $30)/2 = 25
Effectively we are assuming we only hold one share of A and B, hence the working looks like this (to make it more obvious):
(1 \times 20 + 1 \times 30)/2 = 25
For equally weighted index, we need to ensure the market value of each constituent securities are equal (not price).
So, for securities A and B above, I could for example have 450 shares of A and 300 shares of B, then:
Market value of A = 450 x $20 = $9,000 (Weight = 50%)
Market value of B = 300 x $30 = $9,000 (Weight = 50%)
In an equal-weighted index you have the same value of each stock; in a price-weighted index you have the same number of shares of each stock.
Suppose that stock ABC has a share price of $20 and stock XYZ has a share price of $25. In a price-weighted index you might have, say, five shares of each. In an equal-weighted index, you might have five shares of ABC and four shares of XYZ.